Question

1+3+5+7+...+19=
Este patrat perfect??

Answer 1

Răspuns:

da

Explicație pas cu pas:

1 +  3 +  5  +... + 15 +17 +19=S

19+ 17 + 15 + ... + 3 + 2 + 1 =S

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20+20+20+...+ 20+20+20=2S (20 apare de (19+1):2=10 ori)

20*10=2S

200=2S => S=200:2=100=10², deci e patrat perfect

Answer 2

1 + 3 + 5 + ... + 19 =

[ ( 19 - 1 ) : 2 + 1 ) ] × [ ( 19 + 1 ) : 2 ] =

( 18 : 2 + 1 ) × ( 20 : 2 ) =

( 9 + 1 ) × 10 =

10 × 10 = 100

100 = 10 ^ 2 => pătrat perfect